Which pair of complex numbers has a real-number product?
(1+2 i)(8 i)
(1+2 i)(2-5 i)
(1+2 i)(1-2 i)
(1+2 i)(4 i)
Answer (3)
rap - 1/4 jazz - 3/8 rock - x all - 1
jazz + rap + rock = all
3/8 + 1/4 + x = 1 3/8 + 2/8 + x = 1 5/8 + x = 1 x = 1 - 5/8 x = 3/8
answer: rock - 3/8
a − a ll j − ja zz r a − r a p r c − roc k a = j + r a + r c ⇒ r c = a − j − r a r c = 1 − 8 3 − 4 1 r c = 1 − 8 3 − 8 2 r c = 8 8 − 8 3 − 8 2 r c = 8 3
The fraction of Jasmine's CD collection that is rock music is 8 3 . This is found by subtracting the known fractions of jazz and rap from the total collection. Jazz accounts for 8 3 and rap 4 1 (equal to 8 2 ), leading to 8 3 for rock.
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